Algebraic Solution for $(y - z)^2$
We are given the equations:
- $ (y + z) = 8 $
- $ yz = 6 $
We need to find the value of $ (y - z)^2 $.
Applying Algebraic Identity
We use the algebraic identity that relates $ (y + z)^2 $, $ (y - z)^2 $, and $ yz $: $ (y - z)^2 = (y + z)^2 - 4yz $
Calculation
Substitute the given values into the identity:
$ (y - z)^2 = (8)^2 - 4(6) $
$ (y - z)^2 = 64 - 24 $
$ (y - z)^2 = 40 $
Thus, the value of $ (y - z)^2 $ is 40.
Similar Questions
- If $a + b + c = 10$ and $ab + bc + ca = 31$, find the value of $a^2 + b^2 + c^2$
If $a + b + c = 0$, then find the value of $\frac{(a^2+b^2+c^2)^2}{a^2b^2+b^2c^2+c^2a^2}$
- If $x^4 + \frac{1}{x^4} = 322$, then $x^3 - \frac{1}{x^3} = ?$
- What is the value of the following expression:
$(1 + x)(1 + x^2)(1 + x^4)(1 + x^8)(1 - x)$ - If $a + b + c = 17$, $abc = 168$, and $ab + bc + ca = 94$, then $a^3 + b^3 + c^3 = ?$
- If $a = \frac{b^2}{b - a}$, then the value of $a^3 + b^3$ is:
- If $ab = 10$ and $a^{2} + b^{2} = 29$, then $(a - b)^{2} = ?$
- If $(x + \frac{1}{x}) = 7$, then $(x - \frac{1}{x})$ is equal to:
- Find the value of $\frac{(74 + 47)^2 + (74 - 47)^2}{74^2 + 47^2}$
- If $x = 3 + \sqrt{5}$ and $y = 3 - \sqrt{5}$, then find the value of $x^2 + y^2$.
Important Questions from Identities
(x - y) 3+ (y - z) 3+ (z - x) 3= ?
If \(x + \left( {\frac{1}{x}} \right) = 12\) and \({x^2} - \frac{1}{{{x^2}}} = 50\) , then the value of \({x^4} - \frac{1}{{{x^4}}} \) is:
- \((\sqrt{7} + \sqrt{9})(\sqrt{7} - \sqrt{9})\) is equal to:
If x satisfies the equation x 2 - 2x + 1 = 0, then the value of \(\rm x^3 - \frac{1}{x^3}\) is:
If x + y = 5 and xy = 6, then find x 3+ y 3
